{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:6HCKP4UNJ3IM2QEEQ7SNXQMEVK","short_pith_number":"pith:6HCKP4UN","schema_version":"1.0","canonical_sha256":"f1c4a7f28d4ed0cd408487e4dbc184aa9ccf016651a0c74a8b8fea7652716546","source":{"kind":"arxiv","id":"2606.06280","version":1},"attestation_state":"computed","paper":{"title":"Second order splitting dynamics for stochastic monotone inclusions with closed loop distribution","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hamza Ennaji, Jalal Fadili, Wutao Si","submitted_at":"2026-06-04T15:22:44Z","abstract_excerpt":"In this paper, we investigate the problem of finding a zero of the sum of a maximal monotone operator $A$ and a cocoercive operator $\\Bm$ in a Hilbert space. This formulation naturally captures stochastic optimization problems with decision-dependent distributions, often referred to as performative prediction. We propose and analyze continuous-time second-order dynamics governed by a distributionally evaluated forward-backward splitting operator. We establish the existence and uniqueness of the equilibrium point under a general uniform monotonicity assumption. In this setting, employing a vani"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.06280","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-06-04T15:22:44Z","cross_cats_sorted":[],"title_canon_sha256":"55680588adcd0bd7309d00325aeff6ebbbc8d6d565cef4c6d999bd94a2c90825","abstract_canon_sha256":"1d12f2b232e9cd99ed945762a311fc8f9091bd1b2329c1e57936d121b0a27c6f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-05T01:15:40.417017Z","signature_b64":"Gbb7snKnuVH+AeK1aAxuHCyQdk4j5EQvLvv6A1G7/bv28k2sIDOX1ScMoqxo3/L2HaekfOqELAqyc+UQvjf8CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1c4a7f28d4ed0cd408487e4dbc184aa9ccf016651a0c74a8b8fea7652716546","last_reissued_at":"2026-06-05T01:15:40.416633Z","signature_status":"signed_v1","first_computed_at":"2026-06-05T01:15:40.416633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Second order splitting dynamics for stochastic monotone inclusions with closed loop distribution","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hamza Ennaji, Jalal Fadili, Wutao Si","submitted_at":"2026-06-04T15:22:44Z","abstract_excerpt":"In this paper, we investigate the problem of finding a zero of the sum of a maximal monotone operator $A$ and a cocoercive operator $\\Bm$ in a Hilbert space. This formulation naturally captures stochastic optimization problems with decision-dependent distributions, often referred to as performative prediction. We propose and analyze continuous-time second-order dynamics governed by a distributionally evaluated forward-backward splitting operator. We establish the existence and uniqueness of the equilibrium point under a general uniform monotonicity assumption. In this setting, employing a vani"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06280","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.06280/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.06280","created_at":"2026-06-05T01:15:40.416695+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.06280v1","created_at":"2026-06-05T01:15:40.416695+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06280","created_at":"2026-06-05T01:15:40.416695+00:00"},{"alias_kind":"pith_short_12","alias_value":"6HCKP4UNJ3IM","created_at":"2026-06-05T01:15:40.416695+00:00"},{"alias_kind":"pith_short_16","alias_value":"6HCKP4UNJ3IM2QEE","created_at":"2026-06-05T01:15:40.416695+00:00"},{"alias_kind":"pith_short_8","alias_value":"6HCKP4UN","created_at":"2026-06-05T01:15:40.416695+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6HCKP4UNJ3IM2QEEQ7SNXQMEVK","json":"https://pith.science/pith/6HCKP4UNJ3IM2QEEQ7SNXQMEVK.json","graph_json":"https://pith.science/api/pith-number/6HCKP4UNJ3IM2QEEQ7SNXQMEVK/graph.json","events_json":"https://pith.science/api/pith-number/6HCKP4UNJ3IM2QEEQ7SNXQMEVK/events.json","paper":"https://pith.science/paper/6HCKP4UN"},"agent_actions":{"view_html":"https://pith.science/pith/6HCKP4UNJ3IM2QEEQ7SNXQMEVK","download_json":"https://pith.science/pith/6HCKP4UNJ3IM2QEEQ7SNXQMEVK.json","view_paper":"https://pith.science/paper/6HCKP4UN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.06280&json=true","fetch_graph":"https://pith.science/api/pith-number/6HCKP4UNJ3IM2QEEQ7SNXQMEVK/graph.json","fetch_events":"https://pith.science/api/pith-number/6HCKP4UNJ3IM2QEEQ7SNXQMEVK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6HCKP4UNJ3IM2QEEQ7SNXQMEVK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6HCKP4UNJ3IM2QEEQ7SNXQMEVK/action/storage_attestation","attest_author":"https://pith.science/pith/6HCKP4UNJ3IM2QEEQ7SNXQMEVK/action/author_attestation","sign_citation":"https://pith.science/pith/6HCKP4UNJ3IM2QEEQ7SNXQMEVK/action/citation_signature","submit_replication":"https://pith.science/pith/6HCKP4UNJ3IM2QEEQ7SNXQMEVK/action/replication_record"}},"created_at":"2026-06-05T01:15:40.416695+00:00","updated_at":"2026-06-05T01:15:40.416695+00:00"}